Mach Stem Modeling with Spherical Shock Waves

A semiempirical model was developed for the treatment of the Mach stem region of a nuclear airburst. This model predicts the conditions that would be observed by an aircraft or missile as well as the limits of this region in space. The model is based upon current shock theory. Where three shock theory fails to accurately predict physical reality, new relations are developed or empirical data is used. Specifically, this model predicts the path of the triple point, the overpressure, dynamic pressure, time of arrival, and direction of the shock impulse above the ground. An explanation of the development of each prediction is made and compared to actual nuclear or high explosive test data. Additionally, a comparison is made between conventional Mach stem modeling and this model. Unique to this model is a method fo predicting the variation of pressure with altitude above the ground. For low scaled heights of burst, the overpressure found at an altitude of 20 of the triple point height is greater than that on the ground. In addition, the overpressure measured just below the triple points if found to be only 60 of the ground overpressure scaled to altitude. This prediction is radically different than conventional ground overpressures scaled to atmospheric pressure at altitude. The predictions made by this model are verified by nuclear and high explosive test data.